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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 2v, page id 00068072:0004
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 sint circuli ordinatim datri, quorum
Centra in curva V(V), et, dalo puncto curvae i,
 inte Horum circulorum intersectine
formetur curva  Y (3
Exnatura cioculi AX, X
CyV v. VVOr. ZZ E=X + y -o L) rr. et pro
concurtu circularum (2 - X) dX + (y- 0) du  rar Et ex
Circuli langentit, (Z- X) dx + (y- V) dy =0 seu Ddx: dy=
Z-Y
soeiitis
3)
v.y fat sit jam aequatio data: Ax: dus = t: a
Z- X9:, v- y  (6to) F: a. jam ex aqu. 1,F, 1 et 2, inveniantur
X ot Y, et substituantur in aequib Rursus jam ex aequ. 1. et 2. Invenians
E
X et y, fi et substituantur in aequ. 6, habebitur aequ. inqua
solum Z, v, Y, dz dv, dr., Nempe ex 2 est
v
y - v = Y ar - (Z- X) ax, :dv  = 1(rr -(Z -X) 2) et seu
YX(drdr: d vdv) + (Z- x) 2 (dX dx: dvav) C 2Y (Z X) (drdx: de dx)  rr-β X) =
seu (Z-X) = - 2rd rdx (y- X) + erdrar dede guextrrade + rrdrardudx
qdx+ axdip
12) (ax X+ dvar) ( (dx dx + dvdv)
BY,  drax + savire  L + dB Fararae 3
et fit R Z-x =  s 
10
seu X = Z = Y
Cardx + sevdv (de d3 Favdn fF ardrdZaZ) x de + dudx
az dz + dx do
et parijure V -g = Y ardio + fl 2de C   +dvdu) + arar av ilo)
az z+ av du
seu y 0 - Y. drdv + (ddqze (d2A Z favdr) + drar dudv)
dz d2 F dudo
g, et 1I, fiet
et fit et ex aequ. per
+ (3) araque + Y (do dv (d Zdz +do dv) + drdr dzd2)
a
in aeg. 13 drdv F Y (dZdZ (dZ +Z + dvdv) + drdr dvdv)
Et quia explicando  per X. a, y: a et ex datis secundum aequ. 5.
et in aeq. ut fiat aequ. 14 et in ea pro X, y, substi tiendo valores
ex aequeo 10 et 12. habebitur aequ. inter Z, v, du, dv, r, dr,d
si si b + a expli compendio sid r d Z + (+a (d 2 1Z+ dvdr) + ardr dezu)  dsu
et idem permulatis solum dZe et de sit, = (16) dgdus et dZ dv + dv dv sitsos) - dede
fiet ex 13, t: a = (18) afdf: dgclus et  = 10, X = (19) Z - Y (fdf: dede)
et ex 12, y = (20) v- r (dydg; dece) aequatio data 5, t: a Xxtgy,iaa
Au (22
seu xx. per 18, XX+yy, : aa=dfds: eg dodus, et fice et ope
e +rdsErZede d, dodo =aa dsaf de 4+
Edg+ Zero Eyd9s c
aegg. 19 et 20, ex aeq. 22. fiet 
videamus an licuat facere (24) df =0 seu de
seu ex
15, Card raz d2) = dZ dz (d ZdZ+ Lodo)  dr+rdzdZ et fiet
vel dZ du Ya  quod est impossibile, vel aq
seu ex eg. 15. Cdrdr dz d2 = dodo (d2d, + dodo) (+ drardydu 
adeoque de = dz f- 1. sed ia fieret et de=. unde praestaret potius
onservare df. sed video posito de=o tamen huc tandem veniti d
aliter = faadtas XXdgs idg , seu Ly = Ma d fa sde - 27d0.  2Er dedeatat 
22
:dg = v - r(dgda: dede)
si loco aqu. 22. fuisse
fieret ex ig et 20, Z- 2+ ZEde +rrds - 2Zr dededsls  rta: +X 
24)
vode-rrdgt +vY dydegus d agag=na dfils do +
ubi faciendo Z v = 0 fiet YYdf4 - rraq, dodus = aa d fd+ dC
Ex 24 sit dZ = dv
et dfdf. per 15 = C 17) draz + de N(2 dxd +drar) = (28) iudusddb. Et ex aequ.
25 fit redes rrdSE er de sed ob aeg. 29. in ipsa 25 dvavescent Omnia, et
fiet af sel de =0,  de non dede = 0 non licet Ergo fiat df =0 sit ita fieret y=0
et X -Z et y- X. quo non licet facere